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Testing a sub-hypothesis in linear regression models with long memory covariates and errors

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Abstract

This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be n 1/2-consistent for all values of the long memory parameters of the design and error processes.

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References

  1. R. Baillie: Long memory processes and fractional integration in econometrics. J. Econom. 73 (1996), 5–59.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. G. Booth, R. R. Kaen, P. E. Koves: R/S analysis of foreign exchange rates under two international money regimes. J. Monet. Econom. 10 (1982), 4070–415.

    Google Scholar 

  3. J. Beran: Statistical methods for data with long-range dependence (with discussion). Stat. Sci. 7 (1992), 404–427.

    Article  Google Scholar 

  4. J. Beran: Statistics for Long Memory Processes. Monographs on Statistics and Applied Probability, Vol. 61. Chapman and Hall, London, 1994.

    MATH  Google Scholar 

  5. Y.-W. Cheung: Long memory in foreign exchange rates. Journal of Business and Economic Statistics 11 (1993), 93–101.

    Article  Google Scholar 

  6. Empirical Process Techniques for Dependent Data (H. Dehling, T. Mikosch, M. Sørensen, eds.). Birkhäuser, Boston, 2002.

    MATH  Google Scholar 

  7. Theory and Applications of Long-Range Dependence (P. Doukhan, G. Oppenheim, M. S. Taqqu, eds.). Birkhäuser, Boston, 2003.

    MATH  Google Scholar 

  8. R. Fox, M. S. Taqqu: Large-sample properties of parameter estimates for strongly dependent Gaussian time series. Ann. Stat. 14 (1986), 517–532.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Giraitis, D. Surgailis: A central limit theorem for quadratic forms in strongly dependent linear variables and its applications to asymptotical normality of Whittle’s estimate. Prob. Theory Relat. Fields 86 (1990), 87–104.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Guo, H. L. Koul: Nonparametric regression with heteroscedastic long memory errors. J. Stat. Plann. Inference 137 (2007), 379–404.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. J. Hannan: The asymptotic theory of linear time-series models. J. Appl. Probab. 10 (1973), 130–145.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. D. Hart: Nonparametric Smoothing and Lack-of-Fit Tests. Springer Series in Statistics. Springer, New York, 1997.

    Google Scholar 

  13. J. Hidalgo, P. M. Robinson: Adapting to unknown disturbance autocorrelation in regression with long memory. Econometrica 70 (2002), 1545–1581.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. L. Koul, D. Surgailis: Asymptotic normality of the Whittle estimator in linear regression models with long memory errors. Stat. Inference Stoch. Process. 3 (2000), 129–147.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. W. Lo: Long term memory in stock market prices. Econometrica 59 (1991), 1279–1313.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. R. Rao: Linear Statistical Inference and Its Applications. Wiley, New York, 1965.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, A435 Wells Hall, East Lansing, MI, 48824, USA

    Hira L. Koul

  2. Vilnius Institute of Mathematics and Informatics, 2600, Vilnius, Lithuania

    Donatas Surgailis

Authors
  1. Hira L. Koul
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  2. Donatas Surgailis
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Corresponding author

Correspondence to Hira L. Koul.

Additional information

Research of the first author was partly supported by the NSF DMS Grant 0701430. Research of the second author was partly supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation grant T-15/07.

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Koul, H.L., Surgailis, D. Testing a sub-hypothesis in linear regression models with long memory covariates and errors. Appl Math 53, 235–248 (2008). https://doi.org/10.1007/s10492-008-0007-z

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